Jon Heyman of CBSSports.com first reported that New York declined a trade offer for Phillips in exchange for outfielder and potential leadoff hitter Brett Gardner. Heyman also reported that Phillips asked for his contract to be reopened to give him more money to agree to a trade.

A person with knowledge of the Yankees' thinking said that reports of the discussions about a deal involving Phillips and Gardner were "way overblown."

The person said that the Yankees do not plan on trading Gardner, saying, "[If they did,] it would have to be in a valuable pitching capacity."

An MLB.com source revealed the Yankees are one of the teams listed in Phillips' limited no-trade clause. The Reds would need his approval before they could deal him to the Yankees.

New York has a void at second base after losing out on re-signing Robinson Cano, who agreed to a 10-year contract with the Mariners. The Yankees have touched base with free agent Omar Infante as a possible replacement.

The Reds, who expect to lose free agent Shin-Soo Choo, are in need of a center fielder and leadoff hitter with a short-term contract that can let them take their time to develop prospect Billy Hamilton.

Gardner, who batted .273 with a .344 on-base percentage in 145 games last season, is arbitration-eligible for a third time and can become a free agent after the 2014 season.

Phillips, 32, has four years and $50 million remaining on his contract. In 2013, he batted .261 with 18 home runs, 103 RBIs and a .310 on-base percentage.

Reds general manager Walt Jocketty told Phillips last week he was not actively shopping Phillips for a trade, but he did also say he would look at opportunities if they're presented.

Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.